Three tasks were conducted for the implementation of the proposed model: identifying road groups, developing and executing the artificial neural networks, and calculating AADT.
7.3.1 Establishing Road Groups Using Fuzzy C-Means
PTCs data from the 42 AVCs were used to establish the road groups (see
k, following Eq. 6.1. Then the Fuzzy C-means algorithm was applied using
the adjustment factors as inputs. The algorithm was tested by changing the
values of C from 2 to 20, running the algorithm for different time periods
(10), changing the starting point and verifying the stability of results. The best number of groups was chosen by comparing the values of four indices:
• the Dunn Index;
• the Silhouette measure; • the Pseudo F Statistic;
• Goodman and Kruskal’s index G2.
Based on these criteria, the best number of groups C∗was found to be
8 for the case study. For each AVC k the membership grades to each road
group uij(Table 7.4) were analysed with the procedure presented in section
6.1 and the belonging to a Road Group was determined.
Table 7.4:Membership Grades of the AVCs to Different Road Groups
AVC Number Group1 Group 2 Group 3 Group 4 Group 5 Group 6 Group 7 Group8 Road Group
1 0.01 0.01 0.01 0.03 0.91 0.02 0.00 0.01 5 2 0.01 0.01 0.01 0.04 0.05 0.79 0.01 0.08 6 3 0.05 0.02 0.04 0.78 0.04 0.05 0.01 0.01 4 4 0.03 0.01 0.02 0.87 0.03 0.02 0.01 0.01 4 5 0.19 0.17 0.60 0.02 0.01 0.01 0.00 0.00 3 6 0.07 0.03 0.90 0.00 0.00 0.00 0.00 0.00 3 7 0.02 0.01 0.01 0.06 0.81 0.05 0.01 0.03 5 8 0.01 0.01 0.01 0.02 0.02 0.91 0.00 0.02 6 9 0.61 0.09 0.26 0.02 0.01 0.01 0.00 0.00 1 10 0.62 0.08 0.26 0.02 0.01 0.01 0.00 0.00 1 11 0.66 0.06 0.25 0.02 0.01 0.00 0.00 0.00 1 12 0.68 0.07 0.21 0.02 0.01 0.01 0.00 0.00 1 13 0.85 0.04 0.10 0.01 0.00 0.00 0.00 0.00 1 14 0.33 0.09 0.26 0.25 0.04 0.02 0.00 0.01 (1, 3, 4) 15 0.32 0.09 0.25 0.26 0.03 0.03 0.01 0.01 (1, 3, 4) 16 0.47 0.09 0.40 0.03 0.01 0.00 0.00 0.00 (1, 3) 17 0.40 0.10 0.45 0.03 0.01 0.01 0.00 0.00 (1, 3) 18 0.32 0.10 0.26 0.25 0.03 0.03 0.00 0.01 (1, 3, 4) 19 0.08 0.74 0.14 0.02 0.01 0.01 0.00 0.00 2 20 0.08 0.76 0.13 0.02 0.01 0.00 0.00 0.00 2 21 0.12 0.08 0.79 0.01 0.00 0.00 0.00 0.00 3 22 0.14 0.13 0.69 0.02 0.01 0.01 0.00 0.00 3 23 0.08 0.77 0.12 0.02 0.01 0.00 0.00 0.00 2 24 0.10 0.72 0.13 0.02 0.01 0.01 0.00 0.01 2 25 0.13 0.27 0.56 0.02 0.01 0.01 0.00 0.00 3 26 0.14 0.22 0.60 0.02 0.01 0.01 0.00 0.00 3 27 0.08 0.05 0.86 0.01 0.00 0.00 0.00 0.00 3 28 0.12 0.16 0.71 0.01 0.00 0.00 0.00 0.00 3 29 0.26 0.16 0.54 0.03 0.01 0.00 0.00 0.00 3 30 0.15 0.06 0.76 0.01 0.01 0.01 0.00 0.00 3 31 0.36 0.28 0.28 0.05 0.01 0.01 0.00 0.01 (1, 2, 3) 32 0.27 0.27 0.36 0.05 0.02 0.02 0.00 0.01 (1, 2, 3) 33 0.01 0.01 0.01 0.04 0.89 0.03 0.00 0.01 5 34 0.01 0.01 0.01 0.04 0.04 0.86 0.00 0.03 6 35 0.09 0.05 0.07 0.63 0.09 0.05 0.00 0.02 4 36 0.00 0.00 0.00 0.04 0.00 0.00 0.89 0.07 7 37 0.01 0.01 0.01 0.02 0.02 0.05 0.00 0.88 8 38 0.06 0.78 0.15 0.01 0.00 0.00 0.00 0.00 2 39 0.00 0.00 0.00 0.00 0.01 0.03 0.90 0.06 7 40 0.01 0.00 0.01 0.01 0.02 0.00 0.05 0.90 8 41 0.78 0.05 0.14 0.02 0.01 0.00 0.00 0.00 1 42 0.80 0.04 0.13 0.02 0.01 0.00 0.00 0.00 1
The seasonal adjustment factors that correspond to (i, j) combinations
were calculated for the C∗road groups with Equation 6.3. Reciprocals of the
seasonal adjustment factors r fijcwere defined by:
r fijc=
1
fijc
(7.1) and they could represent the characteristics of fluctuations better than
the seasonal adjustment factor, fijc. Average seasonal adjustment factors of
the road groups and their reciprocals are reported in Tables A.2 and A.3 in Appendix. In Figure 7.1 the average reciprocals of the seasonal adjustment
factors r fijcfor different days and periods of the year are plotted for each
road group.
Figure 7.1:Reciprocals of the Seasonal Adjustment Factors for the Road Groups
Analysing the plot some clearly distinguishable traffic patterns can be
observed:
• Groups 1 (7 AVCs), 2 (5 AVCs), and 3 (10 AVCs) could be characterized
as commuter road groups. These groups show stable traffic patterns,
with seasonal adjustment factors close to one, in particular for week- days. Weekly traffic patterns occur in similar manner during the year,
but some differences exist among groups:
– Group 1 passenger car volumes increase from weekdays to Sat-
– Group 2 shows a pattern similar to Group 1, but the decrease ob- served during Sundays is more relevant, in particular in summer
period (seasonal adjustment factors SunMay/Junand SunJul/Aug);
– Group 3 pattern is characterised by a decrease of traffic volumes
during week-ends, in particular on Sundays.
• Groups 5 (3 AVCs), 6 (3 AVCs), 7 (2 AVCs) and 8 (2 AVCs) could be
characterized as recreational road groups. Traffic patterns are charac-
terised by a strong variability during the year: very small volumes in winter period and high peaks in summer time, with higher variations observed for Groups 7 and 8.
A deeper analysis of the composition of the groups shows that the
AVCs of the same site belong to different groups: Group 5 - Group 6 or
Group 7 - Group 8. This fact is due to different traffic patterns observed in each direction during summer week-ends (May/Jun and Jul/Aug):
Groups 5 and 7 have peaks in traffic volumes during Saturdays, while
Groups 6 and 8 have their peaks during Sundays.
These differences can be explained considering the holiday trips made by people during week-ends: the vacationers reach the holiday resorts on Saturdays and go back home in Sundays driving in the opposite direction.
• Group 4 includes 3 ATRs with intermediate characteristics.
• Seven AVCs were classified as ”I don’t know” cases. They belonged to Group ”1 or 2 or 3” (2 AVCs), Group ”1 or 3”(2 AVCs), Group ”1 or
3 or 4”(3 AVCs), that is they had traffic patterns similar to commuter
roads.
Furthermore spatial distribution of road groups were analysed, to eval-
uate if the differences among road groups could also be interpreted based
on the knowledge of land-use characteristics.
As can be observed in Figure A.4 reported in the Appendix, AVCs were grouped following clear spatial patterns which confirmed previous observations:
• AVCs belonging to commuter road groups (1, 2, 3) are located in the inland parts of the province, where tourist activities are limited and traffic patterns are supposed to be quite stable during the year; • AVCs belonging to recreational road groups (5, 6, 7, 8) are located in
the coastal part of the Province of Venice (groups 7 and 8) or to roads which give access to the tourist facilities (groups 5 and 6). This means that in summer period these roads are supposed to be characterised by very high passenger car volumes compared to winter period;
• AVCs belonging to road group 4 are representative of intermediate characteristics between commuter and recreational roads. Their loca- tion in the road network (between the inland and the coastal line) confirms these characteristics;
• AVCs classified as ”I don’t know cases”, which are characterised by commuter-type patterns, are in the inland parts of the Province.
7.3.2 Developing the Artificial Neural Networks
Multi-layered, feed-forward artificial neural networks (ANNs) were de- veloped in order to assign the SPTCs to the road groups (see section 6.2).
Different structures of ANN are adopted, corresponding to the different SPTCs combinations analysed, as reported in Table 7.5. Applying the pro- posed approach to the case study, the number of output nodes was reduced to 11, since in the training dataset 8 road groups and 3 ”I don’t know” situa- tions were found. Moreover different ANNs were trained for each datasets, maintaining the structure corresponding to the specific duration of SPTCs used. That is 24hr SPTCs taken on weekdays were used to train a network, while 24hr SPTCs taken on Saturdays were used for another network with the same structure.
Table 7.5:Characteristics of ANNs Used for the Assignment
Datasets SPTCs Duration Input Nodes Hidden Nodes Output Nodes
1,2,3 24hr 25 30 11
4,5 48hr 49 60 11
6,7 72hr 73 84 11
Some further details about the training process, repeated in the different
training datasets, are:
• Learning cycles = 25,000; • Momentum α = 0.2; • Learning rate η = 0.3.
7.3.3 Calculation of AADT
In this process each SPTC in the test dataset is assigned by the corre- sponding ANN, obtaining the probabilities of belonging to each road group. The SPTC volume is used to estimate the AADT following only Equation 6.7 for 24hr SPTCs and also Equation 6.8 in case of 48hr and 72hr SPTCs.